Question

Suppose X ∼ Uniform(−1, 1) (a) Find the CDF of X. (b) Use (a) to find the CDF of W = |X| [Tip: if W ≤ w, what does it imply about X?] (c) Use (a) to find the CDF of V = X^2 . [Tip: if V ≤ v, what does it imply about X?] (d) By comparing CDFs of W and V to the Uniform(a, b) CDFs, [or by differentiating and comparing PDFs], which is still uniformly distributed: W or V?

Name: suppose x uniform1 1 a find the cdf of x b use a to find the cdf of w x tip if w w what does it imply about x c use a to find the cdf of v x2 tip if v v what does it imply about x d by compa 99833
Uploaded: 2021-06-14T04:49:58-08:00
Duration: 1 min 50 s
Channel: Wendi Zhao
Description: suppose x uniform1 1 a find the cdf of x b use a to find the cdf of w x tip if w w what does it imply about x c use a to find the cdf of v x2 tip if v v what does it imply about x d by compa 99833

          Suppose X ∼ Uniform(−1, 1)
(a) Find the CDF of X.
(b) Use (a) to find the CDF of W = |X|
[Tip: if W ≤ w, what does it imply about X?]
(c) Use (a) to find the CDF of V = X^2
. [Tip: if V ≤ v, what does it imply about X?]
(d) By comparing CDFs of W and V to the Uniform(a, b) CDFs, [or by differentiating
and comparing PDFs], which is still uniformly distributed: W or V?

Added by Jacqueline J.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Wendi Zhao

06/14/2021

Step 1

In this case, a = -1 and b = 1. Therefore, the CDF of X is F(x) = (x - (-1)) / (1 - (-1)) = (x + 1) / 2 for -1 ≤ x ≤ 1. Show more…

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Suppose X ∼ Uniform(−1, 1) (a) Find the CDF of X. (b) Use (a) to find the CDF of W = |X| [Tip: if W ≤ w, what does it imply about X?] (c) Use (a) to find the CDF of V = X^2 . [Tip: if V ≤ v, what does it imply about X?] (d) By comparing CDFs of W and V to the Uniform(a, b) CDFs, [or by differentiating and comparing PDFs], which is still uniformly distributed: W or V?